solve the following equation on the interval 0<=x<=2pi, csc^2(x) - csc(x)-2=0

Answer 1

csc²(x) - csc(x) - 2 = 0; (csc(x) + 1)(csc(x) - 2) = 0; csc(x) = - 1 or csc(2x) = 2;

x = 3π/2; 2x = π/6, 2x = 5π/6, 2x = 13π/6, 2x = 17π/6;

x = 3π/2; x = π/12, x = 5π/12, x = 13π/12, x = 17π/12